It is proposed to develop certain statistical methodology for analysis of response-time data, often referred to as survival data. Such data are central to many areas of health-related research, especially for time-to-tumor in cancer research. The particular methodology to be developed is that of goodness-of-fit tests pertaining to regression-type models for censored response-time data, and also that relating to the evaluation of efficiency of distribution-free analyses using proportional hazards models. Applications will be made to various sets of cancer data, including time to spontaneous mammary tumors for mice maintained on diets of varying fat compositions.